In a more recent development, there has been renewed interest in the field theoretic and hydrodynamic anomalies with non-zero torsion (and relatedly, so-called pseudo gauge fields) in systems with independent frame fields and connection, in contrast to the metric. Several authors have considered non-zero torsional transport coefficients, given some assumptions beyond standard relativistic field theory and/or finite chemical potential and temperature [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}. The independent gravitational anomaly term from torsion [21]}, [22]}, [23]}, the Nieh-Yan anomaly term [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, is special in that it's 2nd order in the gradients, in contrast to the 4th mixed \(R^2\)  gravitational anomaly from topological anomaly polynomials, and appears with a dimensionful scale parameter that is, apparently, non-universal and unquantized. With considerable past and more recent history, many authors have argued for and against this term with varying and contrasting results, especially whether a dimensionful ultraviolet (UV) scale can appear in the anomaly coefficient. Here we are contend to remark that this term is bound to vanish in relativistic systems, since there is a counter term available that breaks no additional symmetries, while apriori such a term is possible in non-relativistic systems with a cutoff scale to low-energy chiral transport and fermions. See the experimental identification of this chiral anomaly [30]}, [31]} and how it can be matched consistently with the torsional anomaly both at zero and finite temperatures [10]}, [15]}.
